It is desirable to scan the contents of objects at security and customs checkpoints to gain information about content, for example to obtain an indication that the contents of the object do not constitute a threat to security or a breach of customs regulations. It is also desirable to scan the contents of objects for other purposes such as quality control, content verification, degradation monitoring etc.
It is known that information useful in this regard may be obtained from a spectroscopic analysis of radiation received at a detector after interaction with an object under test for example by scanning the object from a suitable high energy electromagnetic radiation source, collecting emergent radiation at a suitable detector after interaction with the object, and processing the emergent radiation spectroscopically, for example against reference data, to draw conclusions about the composition of the object.
The Beer-Lambert law states that for a beam of photons of energy E with intensity I0 incident on a material with thickness, t (cm), the intensity that emerges isI=I0e−μt  1where μ is the linear attenuation coefficient and is defined as the probability of interaction per unit distance travelled. This has units of cm−1. It is often preferable to work with a mass attenuation coefficient which is the linear attenuation coefficient (μ) divided by the material density (φ. The mass attenuation coefficient
  (      μ    ρ    )therefore has the units g−1cm2. The mass attenuation coefficient, in X-ray physics is also generally denoted by the symbol α, not to be confused with the fine structure constant which also shares this symbol. As used herein α refers to the mass attenuation coefficient, unless otherwise specified. Therefore the Beer-Lambert law expressed in terms of the mass attenuation coefficient is
                    I        =                                            I              0                        ⁢                          ⅇ                                                -                                      μ                    ρ                                                  ⁢                                  (                                      ρ                    ⁢                                                                                  ⁢                    t                                    )                                                              =                                    I              0                        ⁢                          ⅇ                              -                                  α                  ⁡                                      (                                          ρ                      ⁢                                                                                          ⁢                      t                                        )                                                                                                  2      
where the product of the density and the distance (ρt) is defined as the mass thickness, x.
X-rays interact with the matter in a number of ways, which may lead to attenuation of the beam. The three most important methods of interaction are;                Compton Scattering        Photoelectric Effect        Pair production        
Other effects, such as Thompson Scattering, play a smaller role, but which process dominates depends upon the mass absorption characteristics of the medium, which is in turn dependent upon the energy of the photons.
Which of these processes dominates is dependent on the mass absorption characteristics of the target (directly related to the atomic number, Z) and the energy of the X-ray.
At low energies the Photoelectric Effect tends to dominate the linear absorption coefficient (μλ), as the photon energy increases the Compton Effect starts to dominate, until Pair Production occurs and dominates at energy above 1022 keV. As X-ray applications generally use X-ray up to several hundred keV, Pair Production does not occur and the attenuation of the beam is mainly caused by a combination of the other two effects.
Several attempts have been made to accurately describe the attenuation from an element, but all are approximations to real data which make a number of assumptions. One of the most widely accepted texts by Jackson and Hawkes, (DF Jackson and DJ Hawkes, X-ray attenuation coefficients of elements and mixtures; Physics Reports 70 (3) pp 169-233 (1981)), present a method for estimating the linear attenuation coefficient as
                              μ          ⁡                      (                          Z              ,              E                        )                          ≅                  ρ          ⁢                                    N              A                        A                    ⁢          Z          ⁢                      {                                          4                ⁢                                  2                                ⁢                                  Z                  4                                ⁢                                  α                  4                                            +                                                (                                                            mc                      2                                        E                                    )                                ⁢                                  ϕ                  0                                ⁢                                                      ∑                                          nll                      ′                                                        ⁢                                      f                                          nll                      ′                                                                                  +                              σ                KN                            +                                                                    Z                    ⁡                                          (                                              1                        -                                                  Z                                                      b                            -                            1                                                                                              )                                                                            Z                    ′2                                                  ⁢                                                      σ                    SC                    coh                                    ⁡                                      (                                                                  Z                        ′                                            ,                                              E                        ′                                                              )                                                                        }                                      3      
where ρ is the mass density, NA is Avagadro's number, A is the atomic mass, Z the atomic number, α in this case is the fine structure constant, m the electron rest mass, c the speed of light, φ0 is the Thomson classical cross section per atom, fnll, is a collection of terms for the Photoelectric cross section, σKN is the Compton cross section and σsccoh is the Rayleigh scattering cross section of a standard element Z′ at energy
      E    ′    =                    (                              Z            ′                    Z                )                    1        /        3              ⁢          E      .      The fitting parameter b is material dependent, thus the exponent of the atomic number varies.
The Jackson Hawkes method has proved accurate in determining the atomic number of elements, but this approach has limitations as it does not directly lead to quantitative information on the composition of the mixture under investigation. Additionally, the definition of only one effective atomic number, often called Zeff, characterising a material is not valid over wide energy ranges or crucially for mixtures or assemblies containing elements with different atomic numbers. This gives inaccuracies when measuring compounds materials, and does not provide discrimination of compounds which may be engineered to look similar in this one property. This method does provide a useful approximation for some radiation studies, however the functionality is limited.
The detection and identification of concealed items inside bottles, packets, electronic devices etc is of key importance in the security industry. In addition the detection of non conforming products in the manufacturing industry are amongst many key areas where X-ray techniques can be used. The limitations of the above approaches are particularly applicable in such cases.